Distributive randomization: a pragmatic fractional factorial design to screen or evaluate multiple simultaneous interventions in a clinical trial

Table 1 Simulation and analysis scenarios

Scenario group	Designs	k	K	Interventions' probability of success			Analysis	Foresight^b/Estimand	Figure
Scenario group	Designs	k	K	1	2	1 + 2	Analysis	Foresight^b/Estimand	Figure
1	All	2	4	70%	50%	70%	Difference of proportions	Yes/Sample size	2A
		2	4–20						2BCD
		4							2E
		8							2F
2	Distributive, factorial	3–8	5, 10, 15, 20	70%	50%	50%	Logistic regression without interaction	Yes/Sample size	3A
		2, 4, 6, 8	4–20		50%	50%		Yes/Sample size	3B
		2–8			70%	84.5%^a		No/Power	3C
						99%			3D
						70%			3E
					60%	70%			3F
3	Distributive, factorial	2–8	4–20	70%	70%	84.5%^a	Logistic regression without interaction	Yes/Sample size	4A
						99%			4B
						70%			4C
					60%	70%			4D
4	(controlled) Distributive with 0–80% intervention-free control	4	10	70%	70%	84.5%^a	Difference of proportions, or logistic regression, with interaction either absent, or backward selected, or pre-specified, or gated pre-specified	Yes/Sample size	5A
		4	10			70%			5B
		2	20			84.5%^a			5C
		2	20			70%			5D

50% success means no intervention effect (this is the baseline in all scenarios) ^adenotes logit-scale additivity, i.e., expit(2ln(7/3)), which is rounded to 84.5% in the table and 84.48276% in the code implementation ^b"foresight" denotes whether trial size was computed with true assumptions; if so, the quantity of interest is sample size, if not, the quantity of interest is power (i.e., how it is affected by those wrong assumptions), and in the latter case the wrong assumption is that of a single effective intervention with 70% success rate

ISSN: 1471-2288